dnd 5e – Can mage hand to fly up over floor to 10-20 feet?

To float generally means stay in place while not touching the ground, being supported, or suspended. As the spell describes the ability for the hand to move between two points and remain floating, that implies that the hand can also fly.

In past editions there was a distinction between float/hover and flying, as to hover while flying required a skill check, or there were abilities that let you float but not fly.